Question:
Mr. Bobby earns a profit of 120% by selling a TV set for $5082. What was the cost price of the TV set?
Correct Answer
2310
Solution And Explanation
Solution
Finding the cost price if the sale price and profit percent are known
The cost price (CP) can be found using the formula, algebraic method, using shortcut method, and taking the cost price as 100, 200, 300, 400, 500, or whatever you want.
Finding the cost price using the formula when the sale price and profit percent are known
Given, the sale price (SP) = $5082
And, the profit = 120%
Then, the Cost Price (CP) = ?
Formula to find the cost price when the sale price and profit percent are known
Cost Price (CP) = 100/100 + gain% × SP
Thus, the Cost Price (CP)
= 100/100 + 120 × 5082
= 100 × 5082/220
= 508200/220 = 2310
Thus, the Cost Price (CP) = $2310 Answer
Finding the cost price (CP) using the Algebraic Method when the Sale Pric (SP) and the profit percent are given
Let the Cost Price (CP) = m
Here given profit = 120%
Calculation of Profit
Profit is calculated on cost price (CP)
Formula to find the Profit = Profit% of CP
Thus, profit on the cost price of m
= 120% of m
= 120% × m
= 120/100 × m
⇒ Profit = 120 m/100
Calculation of Cost Price (CP)
The Sale Price (SP) = Cost Price (CP) + Profit
⇒ 5082 = m + 120 m/100
⇒ 5082 = 100 m + 120 m/100
⇒ 5082 = 220 m/100
After cross multiplication, we get
5082 × 100 = 220 m
⇒ 220 m = 5082 × 100
⇒ m = 5082 × 100/220
⇒ m = 508200/220 = 2310
⇒ m = 2310
Thus, the Cost Price (CP) = $2310 Answer
Finding the cost price (CP) using Unitary Method by taking the cost price (CP) is equal to 100 when the SP and the profit percent are given
Given, the sale price (SP) = $5082
And, the profit = 120%
Then, the Cost Price (CP) = ?
Let Cost Price (CP) = 100
Thus profit = 120% of 100 = 120
Thus, Sale Price (SP) = Cost Price (CP) + Profit
⇒ Sale Price (SP) = 100 + 120
⇒ Sale Price (SP) = 220
∵ If the Sale Price (SP) is 220, then the Cost Price (CP) = 100
∴ If the Sale Price (SP) is 1, then the Cost Price (CP)
= 100/220
∴ If the Sale Price (SP) is 5082, then the Cost Price (CP)
= 100/220 × 5082
= 100 × 5082/220
= 508200/220 = 2310
Thus, the Cost Price (CP) = $2310 Answer
Shortcut Method to find Cost Price (CP) when SP and profit percent are known
Given, the sale price (SP) = $5082
And, the profit = 120%
Then, the Cost Price (CP) = ?
SP = 220% of CP
⇒ SP = 220/100 × CP
⇒ 5082 = 220 CP/100
After cross multiplication
⇒ 5082 × 100 = 220 CP
⇒ 220 CP = 5082 × 100
⇒ CP = 5082 × 100/220
⇒ CP = 508200/220 = 2310
⇒ CP = $2310 Answer
Similar Questions
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(2) James loses 66% by selling an article for $1074.40. For how much should he sell it to get a profit of 65%?
(3) Mrs. Mary earns a profit of 230% after selling an article for $14883. Find the cost price.
(4) If a shopkeeper gets a loss of 53% by selling 200 kg of rice for $4892.70 then find the cost price of rice.
(5) Find the cost price, if a dealer earns a profit of 380% by selling an article for $36048
(6) In a deal, Mr. Kart earns a profit of 85%. He got a total of $2978.50 in the deal. What was the cost price of this deal?
(7) If a trader gets a loss of 55% by selling 15 bags of fruits for $4864.50 then find the cost price of fruits.
(8) Find the profit percent if Mrs. Julie buys 29 bananas for $1 and sells 28 bananas for $1.
(9) If after selling 5 bags of rice for $1297.20 a shopkeeper gets a loss of 8% then what was the cost price of the rice?
(10) How much percent will a vendor earn if he buys 36 articles for $1 and sells them at a rate of 35 articles per $1?